amongst the Molecules of a Gas. 



85 



them; or we may say that the potential of a particle of 

 mass m at a point distant r from it is given by the equation 



V=A™. 



r 3 



Let us assume that the constant A is of such magnitude 

 that V becomes negligible for values of r greater than a certain 

 length R, which corresponds to the radius of the sphere of 

 action considered in most molecular theories, R being a large 

 multiple of the distance between a molecule and its nearest 

 neighbour and at the same time small compared to sensible 

 distances. R is of the order of magnitude of, say, the thickness 

 of a capillary film. Under these circumstances we can consider 

 each molecule as uniformly distributed through the small 

 region of space round it, which may be said to belong to it. 

 Then any one molecule P may be supposed to be gathered 

 into a particle at its centre, leaving the space which belongs 

 to it in the form of a spherical vacuum, while all the other 

 molecules have been spread out around it into a continuous 

 matter of uniform density p. To find the potential of a finite 

 mass of gas at the centre of P, let us describe a cone of small 

 solid angle 10 with its vertex at P, and terminating at the 

 boundary of the gas AA' ; it cuts off the small area aa' on the 

 surface of the vacuous sphere. Then for the potential at P of 



any element xod distant r from P and of thickness dr we have 

 A" — 3 — ; and therefore for the whole potential of the 

 frustrum aa! A' A, — 



Apw 



C^dr 



Apw log 



H, 



where Va—^ and PA = R l8 



Let Rj=nL, where n is a large number so that Lis a small 

 but sensible length. 



